Precise $^{113}$Cd $\beta$ decay spectral shape measurement and interpretation in terms of possible $g_A$ quenching

TL;DR

This study precisely measured the highly forbidden $^{113}$Cd beta decay spectrum using a bolometer, comparing it with theoretical models to explore possible quenching of the axial-vector coupling constant and improve understanding of nuclear decay processes.

Contribution

It provides the most precise $^{113}$Cd beta spectrum measurement to date and compares it with multiple nuclear models to investigate $g_A$ quenching effects.

Findings

Measured $^{113}$Cd half-life as approximately 7.73 x 10^{15} years.

Found $g_A^{ ext{eff}}$ between 1.0 and 1.2, indicating possible quenching.

Achieved the lowest energy threshold and best energy resolution for this decay.

Abstract

Highly forbidden $\beta$ decays provide a sensitive test to nuclear models in a regime in which the decay goes through high spin-multipole states, similar to the neutrinoless double-$\beta$ decay process. There are only 3 nuclei ($^{50}$V, $^{113}$Cd, $^{115}$In) which undergo a $4^{\rm th}$ forbidden non-unique $\beta$ decay. In this work, we compare the experimental $^{113}$Cd spectrum to theoretical spectral shapes in the framework of the spectrum-shape method. We measured with high precision, with the lowest energy threshold and the best energy resolution ever, the $\beta$ spectrum of $^{113}$Cd embedded in a 0.43 kg CdWO$_4$ crystal, operated over 26 days as a bolometer at low temperature in the Canfranc underground laboratory (Spain). We performed a Bayesian fit of the experimental data to three nuclear models (IBFM-2, MQPM and NSM) allowing the reconstruction of the spectral shape as well as the half-life. The fit has two free parameters, one of which is the effective weak axial-vector coupling constant, $g_A^{\text{eff}}$, which resulted in $g_A^{\text{eff}}$ between 1.0 and 1.2, compatible with a possible quenching. Based on the fit, we measured the half-life of the $^{113}$Cd $\beta$ decay including systematic uncertainties as $7.73^{+0.60}_{-0.57} \times 10^{15}$ yr, in agreement with the previous experiments. These results represent a significant step towards a better understanding of low-energy nuclear processes.